Aperiodic Signals Research Articles

Low-dose radiographic inspection of welding by a novel aperiodic reverse stochastic resonance method

Abstract Low-dose radiographic inspection is a growing trend in industry to minimize radiation risks to humans and the environment. However, reduction in radiation dose often introduces significant noise, which affects image quality and hinders accurate identification of subtle defects. This study addresses this issue by introducing a novel phenomenon called aperiodic reverse stochastic resonance (ARSR), observed in nonlinear systems excited by aperiodic binary signals. ARSR enables simultaneous amplitude amplification and reversal of signals under specific noise conditions. Leveraging ARSR, we propose an image denoising framework for low-dose radiographic inspections. First, a set of projection data is obtained by using Radon transform to reduce the dimensionality of X-ray images from different angles. Then, the projection data is modulated based on the ARSR system. Finally, the image is reconstructed based on the inverse Radon transform. Simulations and experimental comparison results in welding applications validate the effectiveness of the framework, demonstrating significant improvements in image quality for low-dose radiographic defect detection. Unlike advanced methods such as Gaussian filtering, BM3D, and DnCNN, which operate at the pixel level, ARSR performs denoising at the projection data stage, reducing noise impact, preserving original information, and focusing on physical data processing during imaging. This approach enhances the detection of subtle defects, highlighting the potential of stochastic resonance in image processing.

The development of aperiodic and periodic resting-state power between early childhood and adulthood: New insights from optically pumped magnetometers

Neurophysiological signals, comprised of both periodic (e.g., oscillatory) and aperiodic (e.g., non-oscillatory) activity, undergo complex developmental changes between childhood and adulthood. With much of the existing literature primarily focused on the periodic features of brain function, our understanding of aperiodic signals is still in its infancy. Here, we are the first to examine age-related changes in periodic (peak frequency and power) and aperiodic (slope and offset) activity using optically pumped magnetometers (OPMs), a new, wearable magnetoencephalography (MEG) technology that is particularly well-suited for studying development. We examined age-related changes in these spectral features in a sample (N=65) of toddlers (1–3 years), children (4–5 years), young adults (20–26 years), and adults (27–38 years). Consistent with the extant literature, we found significant age-related decreases in the aperiodic slope and offset, and changes in peak frequency and power that were frequency-specific; we are the first to show that the effect sizes of these changes also varied across brain regions. This work not only adds to the growing body of work highlighting the advantages of using OPMs, especially for studying development, but also contributes novel information regarding the variation of neurophysiological changes with age across the brain.

Model selection for spectral parameterization.

Neurophysiological brain activity comprises rhythmic (periodic) and arrhythmic (aperiodic) signal elements, which are increasingly studied in relation to behavioral traits and clinical symptoms. Current methods for spectral parameterization of neural recordings rely on user-dependent parameter selection, which challenges the replicability and robustness of findings. Here, we introduce a principled approach to model selection, relying on Bayesian information criterion, for static and time-resolved spectral parameterization of neurophysiological data. We present extensive tests of the approach with ground-truth and empirical magnetoencephalography recordings. Data-driven model selection enhances both the specificity and sensitivity of spectral and spectrogram decompositions, even in non-stationary contexts. Overall, the proposed spectral decomposition with data-driven model selection minimizes the reliance on user expertise and subjective choices, enabling more robust, reproducible, and interpretable research findings.

Aperiodic small signal stability method for detection and mitigation of cascading failures in smart grids

The occurrence of cascading failures poses significant risks to the stability and reliability of modern smart grids. This article presents a novel hybrid algorithm designed to assess and mitigate these failures. The technique combines advanced clustering algorithms, specifically Affinity Propagation Graph (APG) and Self-Propagating Graph (SPG), to detect critical nodes, and Unified Power Flow Controllers (UPFCs) to provide compensation to grid networks. The algorithm first uses APG to divide the network into clusters and considers the center bus as the critical node. If the center bus is not critical, SPG is applied to identify the critical node. This hybrid approach identifies the critical node in just 0.02 s (for both APG and SPG) and with improved accuracy compared to existing methods. After identifying critical nodes, UPFCs are strategically installed to regulate power flow and reduce the probability of cascading failures, with compensation taking approximately 0.14 s. Simulation results demonstrate the effectiveness of the proposed method in enhancing grid resilience and reducing the likelihood of cascading failures. By strategically deploying UPFCs at critical nodes, this approach ensures resilient grid operation in various scenarios. This research significantly contributes to the development of smart grid technologies by providing a comprehensive framework to address cascading failures in power distribution networks. The proposed method shows potential for improving the reliability and stability of power grids amid changing system dynamics and uncertainties.

Signal Decomposition for Monitoring Systems of Processes

This article is devoted to the problem of signal decomposition into periodic and aperiodic components. According to the proposed approach, there is no need to evaluate the aperiodic component as a difference between the total signal of its periodic components. This research aims to create a general analytical approach that combines the Fourier and Maclaurin series methodologies into a single comprehensive series. As a result, analytical expressions for determining deposition coefficients were established for an aperiodic signal with a monoharmonic overlay. Recurrence relations were established to determine the coefficients of this series. These relations allow direct integrations of the obtained values of integrals to be avoided. The evaluated numerical values of the coefficients are also presented graphically and tabulated. It was proven that the values of these coefficients are universal numbers since they do not depend on the period/frequency of oscillations. The reliability of the proposed approach was confirmed by the fact that the evaluated coefficients are equal to the Fourier series coefficients in the case of a periodic signal. Also, for an aperiodic signal, these coefficients were reduced to the coefficients of the Maclaurin series. The usability of the proposed generalized analytical approach for signal decomposition is for control and monitoring systems of processes.

Human sensorimotor resting state beta events and aperiodic activity show good test–retest reliability

ObjectiveDiseases affecting sensorimotor function impair physical independence. Reliable functional clinical biomarkers allowing early diagnosis or targeting treatment and rehabilitation could reduce this burden. Magnetoencephalography (MEG) non-invasively measures brain rhythms such as the somatomotor ‘rolandic’ rhythm which shows intermittent high-amplitude beta (14–30 Hz) ‘events’ that predict behavior across tasks and species and are altered by sensorimotor neurological diseases. MethodsWe assessed test–retest stability, a prerequisite for biomarkers, of spontaneous sensorimotor aperiodic (1/f) signal and beta events in 50 healthy human controls across two MEG sessions using the intraclass correlation coefficient (ICC). Beta events were determined using an amplitude-thresholding approach on a narrow-band filtered amplitude envelope obtained using Morlet wavelet decomposition. ResultsResting sensorimotor characteristics showed good to excellent test–retest stability. Aperiodic component (ICC 0.77–0.88) and beta event amplitude (ICC 0.74–0.82) were very stable, whereas beta event duration was more variable (ICC 0.55–0.7). 2–3 minute recordings were sufficient to obtain stable results. Analysis automatization was successful in 86%. ConclusionsSensorimotor beta phenotype is a stable feature of an individual’s resting brain activity even for short recordings easily measured in patients. SignificanceSpontaneous sensorimotor beta phenotype has potential as a clinical biomarker of sensorimotor system integrity.

The importance of decomposing periodic and aperiodic EEG signals for assessment of brain function in a global context.

Measures of early neuro-cognitive development that are suitable for use in low-resource settings are needed to enable studies of the effects of early adversity on the developing brain in a global context. These measures should have high acquisition rates and good face and construct validity. Here, we investigated the feasibility of a naturalistic electroencephalography (EEG) paradigm in a low-resource context during childhood. Additionally, we examined the sensitivity of periodic and aperiodic EEG metrics to social and non-social stimuli. We recorded simultaneous 20-channel EEG and eye-tracking in 72 children aged 4-12 years (45 females) while they watched videos of women singing nursery rhymes and moving toys, selected to represent familiar childhood experiences. These measures were part of a feasibility study that assessed the feasibility and acceptability of a follow-up data collection of the South African Safe Passage Study, which tracks environmental adversity and brain and cognitive development from before birth up until childhood. We examined whether data quantity and quality varied with child characteristics and the sensitivity of varying EEG metrics (canonical band power in the theta and alpha band and periodic and aperiodic features of the power spectra). We found that children who completed the EEG and eye-tracking assessment were, in general, representative of the full cohort. Data quantity was higher in children with greater visual attention to the stimuli. Out of the tested EEG metrics, periodic measures in the theta frequency range were most sensitive to condition differences, compared to alpha range measures and canonical and aperiodic EEG measures. Our results show that measuring EEG during ecologically valid social and non-social stimuli is feasible in low-resource settings, is feasible for most children, and produces robust indices of social brain function. This work provides preliminary support for testing longitudinal links between social brain function, environmental factors, and emerging behaviors.

Decomposing neurophysiological underpinnings of age-related decline in visual working memory

Exploring the neural basis of age-related decline in working memory is vital in our aging society. Previous electroencephalographic studies suggested that the contralateral delay activity (CDA) may be insensitive to age-related decline in lateralized visual working memory (VWM) performance. Instead, recent evidence indicated that task-induced alpha power lateralization decreases in older age. However, the relationship between alpha power lateralization and age-related decline of VWM performance remains unknown, and recent studies have questioned the validity of these findings due to confounding factors of the aperiodic signal. Using a sample of 134 participants, we replicated the age-related decrease of alpha power lateralization after adjusting for the aperiodic signal. Critically, the link between task performance and alpha power lateralization was found only when correcting for aperiodic signal biases. Functionally, these findings suggest that age-related declines in VWM performance may be related to the decreased ability to prioritize relevant over irrelevant information. Conversely, CDA amplitudes were stable across age groups, suggesting a distinct neural mechanism possibly related to preserved VWM encoding or early maintenance.

A neurophysiological basis for aperiodic EEG and the background spectral trend

Electroencephalograms (EEGs) display a mixture of rhythmic and broadband fluctuations, the latter manifesting as an apparent 1/f spectral trend. While network oscillations are known to generate rhythmic EEG, the neural basis of broadband EEG remains unexplained. Here, we use biophysical modelling to show that aperiodic neural activity can generate detectable scalp potentials and shape broadband EEG features, but that these aperiodic signals do not significantly perturb brain rhythm quantification. Further model analysis demonstrated that rhythmic EEG signals are profoundly corrupted by shifts in synapse properties. To examine this scenario, we recorded EEGs of human subjects being administered propofol, a general anesthetic and GABA receptor agonist. Drug administration caused broadband EEG changes that quantitatively matched propofol’s known effects on GABA receptors. We used our model to correct for these confounding broadband changes, which revealed that delta power, uniquely, increased within seconds of individuals losing consciousness. Altogether, this work details how EEG signals are shaped by neurophysiological factors other than brain rhythms and elucidates how these signals can undermine traditional EEG interpretation.

Quantifying the performance enhancement facilitated by fractional-order implementation of classical control strategies for nanopositioning

For most nanopositioning systems, maximizing positioning bandwidth to accurately track periodic and aperiodic reference signals is the primary performance goal. Closed-loop control schemes are employed to overcome the inherent performance limitations such as mechanical resonance, hysteresis and creep. Most reported control schemes are integer-order and combine both damping and tracking actions. In this work, fractional-order controllers from the positive position feedback family namely: the Fractional-Order Integral Resonant Control (FOIRC), the Fractional-Order Positive Position Feedback (FOPPF) controller, the Fractional-Order Positive Velocity and Position Feedback (FOPVPF) controller and the Fractional-Order Positive, Acceleration, Velocity and Position Feedback (FOPAVPF) controller are designed and analysed. Compared with their classical integer-order implementation, the fractional-order damping and tracking controllers furnish additional design (tuning) parameters, facilitating superior closed-loop bandwidth and tracking accuracy. Detailed simulated experiments are performed on recorded frequency-response data to validate the efficacy, stability and robustness of the proposed control schemes. The results show that the fractional-order versions deliver the best overall performance.

Fuzzy membership-function-dependent design of aperiodic sample-data control scheme for nonlinear PMSG-based WECS with quantization measurements via refined looped Lyapunov functional

This manuscript investigates the fuzzy memory sampled-data control (MSDC) scheme for the nonlinear permanent magnet synchronous generator (PMSG)-based wind energy conversion system (WECS) with quantization measurements. First, due to the complex nonlinearity, a Takagi-Sugeno (T-S) fuzzy modeling approach is successfully applied to the dynamics of nonlinear PMSG-based WECS. Second, by using the information of both quantized aperiodic sampling pattern and signal transmission delay, an H∞-based fuzzy quantized controller is put forward to ensure the stable performance as well as disturbance suppression index of the considered PMSG model by utilizing the refined looped Lyapunov functional (RLLF) approach. This RLLF perfectly utilizes more realistic information about the time derivative of the fuzzy membership function and actual sampling pattern. Then, two new integral inequalities are introduced to approximate the quadratic integral terms arising from the derivative of RLLF. Next, we establish some less conservative stabilization results in terms of linear matrix inequalities (LMIs) using the constructed RLLF, along with the proposed integral inequalities and fuzzy membership function-dependent (MFD) switching ideas. Finally, the simulation studies of PMGS-based WECS are validated numerically, and then a comparative example is provided to emphasize the superiority and relevance of the suggested approach.

Adaptive Anti-Disturbance Performance Guaranteed Formation Tracking Control for Quadrotor UAVs via Aperiodic Signal Updating

Adaptive Anti-Disturbance Performance Guaranteed Formation Tracking Control for Quadrotor UAVs via Aperiodic Signal Updating

Modeling aperiodic sampling to increase the signal processing bandwidth of the sampling analog optical path

The paper discusses methods of aperiodic optical pulsed signal sampling in photonic analog-digital systems. We describe numerical modeling of aperiodic sampling and a method for reconstructing a spectrally sparse signal from aperiodicly selected samples. The described method is based on minimizing the l1 norm of the spectral representation of the reconstructed signal. Numerical simulations show that using aperiodic sampling, it is possible to reconstruct a spectrally sparse signal in the 5 GHz band using a sampling rate of 500 MS/s. The work also shows that using window functions it is possible to improve the quality of signal reconstruction from pseudo-random samples.

Resting-state EEG signatures of Alzheimer's disease are driven by periodic but not aperiodic changes

Electroencephalography (EEG) has shown potential for identifying early-stage biomarkers of neurocognitive dysfunction associated with dementia due to Alzheimer's disease (AD). A large body of evidence shows that, compared to healthy controls (HC), AD is associated with power increases in lower EEG frequencies (delta and theta) and decreases in higher frequencies (alpha and beta), together with slowing of the peak alpha frequency. However, the pathophysiological processes underlying these changes remain unclear. For instance, recent studies have shown that apparent shifts in EEG power from high to low frequencies can be driven either by frequency specific periodic power changes or rather by non-oscillatory (aperiodic) changes in the underlying 1/f slope of the power spectrum. Hence, to clarify the mechanism(s) underlying the EEG alterations associated with AD, it is necessary to account for both periodic and aperiodic characteristics of the EEG signal. Across two independent datasets, we examined whether resting-state EEG changes linked to AD reflect true oscillatory (periodic) changes, changes in the aperiodic (non-oscillatory) signal, or a combination of both. We found strong evidence that the alterations are purely periodic in nature, with decreases in oscillatory power at alpha and beta frequencies (AD < HC) leading to lower (alpha + beta) / (delta + theta) power ratios in AD. Aperiodic EEG features did not differ between AD and HC. By replicating the findings in two cohorts, we provide robust evidence for purely oscillatory pathophysiology in AD and against aperiodic EEG changes. We therefore clarify the alterations underlying the neural dynamics in AD and emphasize the robustness of oscillatory AD signatures, which may further be used as potential prognostic or interventional targets in future clinical investigations.

Human Sensorimotor Beta Event Characteristics and Aperiodic Signal Are Highly Heritable.

Individuals' phenotypes, including the brain's structure and function, are largely determined by genes and their interplay. The resting brain generates salient rhythmic patterns that can be characterized noninvasively using functional neuroimaging such as magnetoencephalography (MEG). One of these rhythms, the somatomotor (rolandic) beta rhythm, shows intermittent high amplitude "events" that predict behavior across tasks and species. Beta rhythm is altered in neurological disease. The aperiodic (1/f) signal present in electrophysiological recordings is also modulated by some neurological conditions and aging. Both sensorimotor beta and aperiodic signal could thus serve as biomarkers of sensorimotor function. Knowledge about the extent to which these brain functional measures are heritable could shed light on the mechanisms underlying their generation. We investigated the heritability and variability of human spontaneous sensorimotor beta rhythm events and aperiodic activity in 210 healthy male and female adult siblings' spontaneous MEG activity. The most heritable trait was the aperiodic 1/f signal, with a heritability of 0.87 in the right hemisphere. Time-resolved beta event amplitude parameters were also highly heritable, whereas the heritabilities for overall beta power, peak frequency, and measures of event duration remained nonsignificant. Human sensorimotor neural activity can thus be dissected into different components with variable heritability. We postulate that these differences partially reflect different underlying signal-generating mechanisms. The 1/f signal and beta event amplitude measures may depend more on fixed, anatomical parameters, whereas beta event duration and its modulation reflect dynamic characteristics, guiding their use as potential disease biomarkers.

EEG microstates in early-to-middle childhood show associations with age, biological sex, and alpha power.

Electroencephalographic (EEG) microstates can provide a unique window into the temporal dynamics of large-scale brain networks across brief (millisecond) timescales. Here, we analysed fundamental temporal features of microstates extracted from the broadband EEG signal in a large (N = 139) cohort of children spanning early-to-middle childhood (4-12 years of age). Linear regression models were used to examine if participants' age and biological sex could predict the temporal parameters GEV, duration, coverage, and occurrence, for five microstate classes (A-E) across both eyes-closed and eyes-open resting-state recordings. We further explored associations between these microstate parameters and posterior alpha power after removal of the 1/f-like aperiodic signal. The microstates obtained from our neurodevelopmental EEG recordings broadly replicated the four canonical microstate classes (A to D) frequently reported in adults, with the addition of the more recently established microstate class E. Biological sex served as a significant predictor in the regression models for four of the five microstate classes (A, C, D, and E). In addition, duration and occurrence for microstate E were both found to be positively associated with age for the eyes-open recordings, while the temporal parameters of microstates C and E both exhibited associations with alpha band spectral power. Together, these findings highlight the influence of age and sex on large-scale functional brain networks during early-to-middle childhood, extending understanding of neural dynamics across this important period for brain development.

Research and application of composite stochastic resonance in enhancement detection

Aiming at the problem that the intermediate potential part of the traditional bistable stochastic resonance model cannot be adjusted independently, a new composite stochastic resonance (NCSR) model is proposed by combining the Woods–Saxon (WS) model and the improved piecewise bistable model. The model retains the characteristics of the independent parameters of WS model and the improved piecewise model has no output saturation, all the parameters in the new model have no coupling characteristics. Under α stable noise environment, the new model is used to detect periodic signal and aperiodic signal, the detection results indicate that the new model has higher noise utilization and better detection effect. Finally, the new model is applied to image denoising, the results showed that under the same conditions, the output peak signal-to-noise ratio (PSNR) and the correlation number of NCSR method is higher than that of other commonly used linear denoising methods and improved piecewise SR methods, the effectiveness of the new model is verified.

Mutual information measure of visual perception based on noisy spiking neural networks.

Note that images of low-illumination are weak aperiodic signals, while mutual information can be used as an effective measure for the shared information between the input stimulus and the output response of nonlinear systems, thus it is possible to develop novel visual perception algorithm based on the principle of aperiodic stochastic resonance within the frame of information theory. To confirm this, we reveal this phenomenon using the integrate-and-fire neural networks of neurons with noisy binary random signal as input first. And then, we propose an improved visual perception algorithm with the image mutual information as assessment index. The numerical experiences show that the target image can be picked up with more easiness by the maximal mutual information than by the minimum of natural image quality evaluation (NIQE), which is one of the most frequently used indexes. Moreover, the advantage of choosing quantile as spike threshold has also been confirmed. The improvement of this research should provide large convenience for potential applications including video tracking in environments of low illumination.

Approximation of Aperiodic Signals Using Non-Integer Harmonic Series: The Generalized NAFASS Approach

In this paper, the non-orthogonal amplitude-frequency analysis of smoothed signals (NAFASS) method) is used to approximate discrete aperiodic signals from various complex systems with the non-integer harmonic series (NIHS). When approximating by the NIHS, there is a problem in determining the dispersion law for harmonic frequencies. In the original version of the NAFASS approach, the frequency dispersion law was determined from a linear-difference equation. However, many complex systems in nature have frequency distributions that differ from the linear law, which is used in the conventional Fourier analysis of periodic signals. This paper proposes a generalization of the NAFASS method for describing aperiodic signals by the NIHS with a frequency distribution that satisfies a recursive formula, which coincides with the local generalized geometric mean (GGM). The methodology of the generalized NAFASS method is demonstrated using descriptions of financial data (prices for metals) and sound data (sounds of insects) as examples. The results show the effectiveness of the generalized NAFASS approach for describing real-world time data. This discovery allows us to propose a new classification scheme for smoothed and aperiodic signals captured as responses and envelopes from various complex systems.

Compressed sampling of gearbox oil temperature signal based on an improved intrinsic mode function basis mixed-dictionary

The oil temperature signal of gearbox is always redundant in long-term use, which will occupy a lot of computer storage space. An improved intrinsic mode function basis mixed-dictionary K-singular value decomposition (IMDK-SVD) algorithm for compressed sampling of the aperiodic oil temperature signal is proposed. Firstly, an improved mixed-dictionary is designed for sparse representation of the aperiodic oil temperature signal, this mixed-dictionary is composed of a class-specific dictionary that extracts the commonness of the same group of data and a shared dictionary that extracts the difference of the different group of data. Secondly, the measurement matrix with variable-step sampling is proposed, and the sampling points is adaptively determined by the information entropy index of signal. Benefitting from these improvements, the advantages of high reconstruction accuracy and saving sampling points as possible are achieved, and the effectiveness of proposed method is verified based on the simulation signal and the experimental signal.